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(a)
pattern 1 ——- 5 = (1 + 1) x 2 + 1
pattern 2 ——- 9 = ( 2 + 2) x 2 + 1
pattern 3 ——- 13 = (3 + 3) x 2 + 1
pattern 4 ——- 17 = (4 + 4) x 2 + 1
pattern 5 ——- (5 + 5) x 2 + 1 = 21

(b)
pattern 1 ——- (1 + 1) x 2 = 4
pattern 2 ——- (2 + 2) x 4 = 16
pattern 3 ——- (3 + 3) x 6 = 36
pattern 4 ——- (4 + 4) x 8 = 64

pattern 8 ——- (8 + 8) x 16 = 256
256 + (8 + 8) x 2 + 1 = 289

(c)

900 = (15 + 15) x 30

Ans : (a) 21 shaded squares; (b) 289 squares; (c) pattern 15.

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for answer c how to get pattern 15, do we need to work out from p8 unitl p15, is there a short cut method to get the value of unshaded pattern no when there is a total of unshaded squares . can you clarifiy

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Please refer to my reply in brackets below,

for answer c how to get pattern 15, do we need to work out from p8 unitl p15, (No) is there a short cut method to get the value of unshaded pattern no when there is a total of unshaded squares . (Yes) can you clarifiy (Yes.

(pattern number + pattern number) x (pattern number x pattern number)

pattern 8 ——- (8 + 8) x 16 = 256

(c)

900 = 30 x 30 = (15 + 15) x 30)

 

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I suggest you take a look at ConceptualMaths’ answer.

He had given the formula for unshaded squares to be n × 2n × 2 where n is the pattern number.

Thus by equating n × 2n × 2 = 900, he found that n = 15

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